Fuel Subsidies, the Oil Market
and the World Economy
Nathan Balke, Michael Plante,
and Mine Yücel
Federal Reserve Bank of Dallas
Research Department
Working Paper 1407
Fuel Subsidies, the Oil Market
and the World Economy
Nathan Balke, Michael Plante and Mine Yucel∗
August 2014
Abstract
This paper studies the effects of oil producing countries’ fuel subsidies on the oil market and the world economy. We identify 24 oil producing countries with fuel subsidies where retail fuel prices are about
34 percent of the world price. We construct a two-country model where
one country represents the oil-exporting subsidizers and the second the
oil-importing bloc, and calibrate the model to match recent data. We
find that the removal of subsidies would reduce the world price of oil
by six percent. The removal of subsidies is unambiguously welfare enhancing for the oil-importing countries. Welfare can also improve in
the oil-exporting countries, depending upon the extent to which they
are net exporters of oil and on oil supply and demand elasticities.
Keywords: oil prices, fuel subsidies, fiscal policy, open economy macro
JEL Classifications: E62, F41, Q43
∗
For helpful comments and suggestions we thank Michael Sposi, Galo Nuno, Kjetil
Storesletten, Christiane Baumeister as well as participants of the USAEE 2013 and 2014
meetings, the 2014 CAMP Workshop and the 2014 Midwest Economics Association conference. Southern Methodist University, [email protected]; Federal Reserve Bank of Dallas, [email protected]; Federal Reserve Bank of Dallas, [email protected].
The views presented in this paper are those of the authors alone and do not reflect the
official views of the Federal Reserve Bank of Dallas or the Federal Reserve System as a
whole.
1
Introduction
Fuel subsidies are used by many developing countries to help lower the cost
of energy for their people. According to the International Energy Agency
(IEA) there were 37 countries with subsidies on oil products for an estimated
total value of $285 billion dollars in 2011. In general, countries which are
net exporters tend to have the largest subsidies. The size of the subsidies
has skyrocketed over the last 10 years. The existence of such large and
widespread subsidies undoubtedly has an effect on oil demand and world oil
prices.
Despite the prevalence of fuel subsidies, there is not a large literature
focusing on them. Several IMF working papers, such as Coady et al. (2006)
and Kpodar (2006), have studied the distributional impacts of removing
fuel subsidies on household expenditures by using social accounting matrix
and input-output models. Hartley and Medlock (2008) studied the behavior
of National Oil Companies (NOC’s) and showed that NOC’s are inefficient
compared to private companies and having the NOC’s subsidize domestic
customers increased this inefficiency. Using a small open-economy model,
Plante (2014) showed that sizable subsidies could introduce significant distortions into the country that put them in place.
What these previous studies miss is the impact that subsidies have on
the world oil market in particular, and on the pattern of world trade in
general. In this paper, we address this gap in the literature by developing
a two-country DSGE model to analyze the effects of fuel subsidies in oil
exporting countries.
In our model we assume both the oil exporters and importers produce
oil, with the oil importers also manufacturing a traded, non-oil good. Oil is
consumed by households in both countries and used in the production of the
non-oil good. The non-oil good is used in oil production and also consumed
by households in both countries.
We identify 24 oil producing countries which have fuel subsidies. We
find that in recent years they consume about 13.5 percent of the world’s oil,
produce nearly 48 percent, and have retail fuel prices around 34 percent of
world prices. To analyze the impact of these subsidies on oil markets and
the global economy, we calibrate our model to match this data. We then
conduct the policy experiment of permanently removing the subsidies on
oil and analyze how this affects the relative price of oil, the consumption
of both oil and non-oil goods, oil production, GDP and welfare in the long
run.
With our benchmark calibration, the results show that removing the
2
subsidies would reduce the world price of oil by about 6 percent. Consumers
in oil exporting countries would re-allocate their consumption away from
fuel products towards other goods while consumers and manufacturers in
the oil-importing country would consume more oil. The removal of the
subsidy and the consequent oil price decline act as a positive oil shock for
the oil-importing country, leading to a small increase in non-oil GDP. We
also analyze how the removal of subsidies affects welfare in both the oil
importing and exporting countries and find that welfare in both countries
increases when the subsidies are removed.
Certain factors are particularly important in determining the results.
These include the elasticities of oil supply and oil demand, as well as the
share of oil production and consumption in the two countries. We explored
the robustness of our results to variations in these factors. The qualitative
nature of our results generally holds for a variety of calibrations, and we
find that removal of the subsidies is welfare enhancing for the oil importing
countries in all cases considered.
On the other hand, in certain cases the removal of subsidies can cause
welfare to fall in the oil-exporting countries. The reason is as follows. Fuel
subsidies artificially increase the world price of oil, and as the subsidizers
are large net exporters of oil they potentially stand to benefit from this
distortion, at the expense of the non-subsidizers. How much they benefit
depends greatly upon the price elasticity of oil import demand of the oil
importers.
For our benchmark calibration, the demand facing the exporting country is elastic, and in this case removing the subsidy is welfare enhancing.
However, the import elasticity of demand becomes smaller when oil supply
and demand are very inelastic. In that case, the revenue consequences of
removing the subsidies becomes less benign for the exporters and removing
the subsidies can reduce their welfare. Essentially, the oil exporting country
is unable to increase its consumption of the non-oil good enough to offset
the decrease in oil consumption brought about by removing the subsidies,
which produces a welfare loss.
The remainder of the paper is organized as follows. We first discuss the
data used in the calibration of the model. In section 3, we introduce a stylized, analytical model to help explain the intuition behind the results of the
paper. Section 4 discusses the two-country DSGE model with endogenous
oil supply. In the context of this model, we examine the effects on the world
economy of removing oil subsidies. We also consider a sensitivity analysis
of these effects to alternative parameterizations of the model. In section 5,
we end with concluding remarks.
3
2
Data
In this section we present data on the subsidizing countries used in our
calibration. We show how important these countries are to the oil market
and how subsidized their prices are in relation to world prices. The data
provide a clearer picture as to why subsidies are an important issue for the
rest of the world. They will also be a key input into the theoretical models
we will use to quantify the importance of these subsidies.
A first step is to decide which oil producing countries to label as subsidizers. We identified 24 countries that we include in the group of subsidizers,
and these countries are listed in table 1. These 24 may be a conservative
estimate. We limited our attention to those countries for which there was
data on retail fuel prices, and for which the data unambiguously pointed to
the presence of fuel subsidies. We also left out a few countries that appear
to only have had intermittent experience with fuel subsidies, such as Mexico
and Brazil.1
In table 2 we show the share of world oil consumption and production
for the group as a whole from 1992 up to 2012. The world oil consumption
and production data come from the Energy Information Administration’s
International Energy Statistics database. We used their annual data on
“Total Petroleum Consumption” and production of “Crude Oil, NGPL, and
Other Liquids” to calculate the consumption and production shares. We
start in 1992 as that is the first year that the data was available for all of
the countries.
Since the early 1990s the share of world oil consumption due to these
countries grew slowly, but steadily. Their share of consumption has risen
from about 9 percent in 1992 to 13.5 percent in 2012. While the share is
not enormous, it is not trivial either. The share of oil produced by these
countries has been between 45 to 50 percent over the sample period. In 2012
the share was almost 48 percent. Taken as a whole, these countries are large
net exporters of oil.
We also need to measure how distorted domestic retail prices in these
countries are compared to world prices. Our data on retail fuel prices come
primarily from two sources: OPEC Annual Statistical Bulletins and the
World Bank’s data on retail gasoline and diesel prices. The former provides
annual averages for retail fuel prices in OPEC member countries, in most
cases from 1990 to 2012. The World Bank data provides bi-annual estimates
1
This number also reflects a lower bound on the total number of countries as it excludes
some oil-importing countries with fuel subsidies. A more complete list of countries can be
found in Plante (2014).
4
of retail fuel prices in a number of other countries, typically starting in 1998.
In a few cases, media reports or other sources, such as the GIZ International
Fuel Price survey, were also used. We describe the exact sources used for
each country in the appendix.
We first choose a benchmark price against which to compare the subsidized prices. We use the national average retail price for gasoline and diesel
in the U.S., excluding taxes, that comes from the U.S. Department of Energy. These prices may not be a perfect benchmark, but since fuel prices in
the U.S. are set in a competitive market, and we have a measure of these
prices that excludes taxes we believe that a large gap between retail prices
in other countries and the U.S. price will almost assuredly be indicative of
subsidization.
Within the context of the models we introduce later, a convenient measure of the degree of subsidization is the ratio between the subsidized price
and the world price. That is, suppose Ps,t is a domestic, subsidized price (in
dollars) at time t while Po,t is the retail price in the U.S. (excluding taxes).
Then one measure of the degree of subsidization is given by
ψt =
Ps,t
.
Po,t
(1)
To construct ψt we need to aggregate across different product prices and
different countries. In doing so, we want to take into account three important
factors. First, gasoline and diesel prices are often subsidized to different
degrees both within and across countries. Second, consumption levels of
gasoline and diesel may also vary within and across countries. Finally, some
of the countries found in table 1 are larger consumers than others.
We perform the following calculations to take these factors into account.
First, in a given year, for each country we calculate one ratio for gasoline
prices and one for diesel prices. Then in each year, for each country, we combine the gasoline and diesel price ratios by weighting them according to the
importance of gasoline consumption, vis-a-vis diesel consumption, in that
particular country. Finally, in a given year we weight each country’s ratio
with that country’s share of oil-consumption relative to the other countries
as a whole, and then sum across all countries to produce ψt .
Using the OPEC data we can construct ψt back to 1990 for 10 countries.
The World Bank data allows us to construct a series from 1998 onwards
for all 24 countries. Figure 1 plots the ratios for the two groups. For the
small set of countries, ψt indicates that they have subsidized prices over the
entire sample period, and that the subsidies have increased significantly over
the last 15 years. In 2012 prices in these countries were just 30 percent of
5
U.S. prices. For the whole set of countries, we find a similar pattern in the
behavior of ψt . In 2012, prices for the 24 countries were 34 percent of those
found in the U.S. 2
The ratio for the whole group is generally higher than the ratio for just
OPEC members, reflecting the fact that certain OPEC members heavily
subsidize fuel products. However, the differences are not particularly dramatic after 1998. The reason for this is that a majority of the oil that is
consumed by the 24 countries is due to just a handful of countries, and they
have price ratios that are very low. For example, in 2012 half of the consumption of oil out of the 24 countries was due to Indonesia, Iran, and Saudi
Arabia, which had price-ratios of .55, .32 and .11, respectively. The next
three largest consumers were Egypt, Iraq, and Venezuela, which had price
ratios of .32, .41, and .02 respectively. As such, the subsidization policies of
these countries dominate the behavior of ψt .
In the next section, we use a simple model to highlight the important
channels through which these subsidies could affect the oil market and the
world economy. In section 4 we introduce a more sophisticated general
equilibrium model which is calibrated to match the data introduced in this
section. We use our calibrated model to gauge the quantitative importance
of the subsidies.
3
Motivating example
In this section we introduce a highly stylized two-country model. The simple setup employed here produces analytical results that explicitly show how
the presence of a subsidy in the oil exporting countries can affect the world
price of oil and the consumption of both oil and non-oil goods. Our goal
here is to highlight the important channels through which subsidies distort
economic variables and highlight what factors may determine the quantitative importance of these distortions. Although the model is very simple
in nature, the findings here provide good intuition for many of the results
found in the more complicated model we introduce in section 4.
3.1
The model
We consider a world where there are two countries, country a and country o.
The latter represents the group of net oil exporters that subsidize domestic
residents’ consumption of fuel products. The former represents the rest
2
The exact numbers were 29.75 percent and 34.27 percent.
6
of the world. In terms of notation, we use superscripts to refer to the
two countries, so that Z o and Z a refer to variable Z in country o and a,
respectively.
Both country a and country o produce oil. Country o’s supply of oil is
given by Yoo , while country a’s production of oil is given by Yoa . Country a
also produces a non-oil good that one can view as manufactures and other
goods that are primarily produced outside of oil exporting countries. The
two goods are consumed by households in both countries. The countries
trade with each other, and country a is a net importer of oil. We assume
the non-oil good is the numeraire and denote the relative price of oil on the
world market as Po .
Total demand for oil in o and a is given by Oo and Oa , respectively.
Demand for oil on the part of country a can be broken down further into
demand due to household consumption, Oca , and demand for oil for use in
production of the non-oil good, Oya , so that Oa = Oca + Oya . However, for
this section we only model the behavior of overall demand Oa . Consumers
in a pay the world price for oil, Po , while consumers in o pay a potentially
subsidized price given by Ps . We define ≥ 0 as the absolute value of the
price-elasticity of demand for fuel products and assume it is the same for
country o and country a. We assume that the supply of oil is responsive to
changes in the world price of oil. The elasticity of supply of oil for country
o and country a is denoted as η o and η a , respectively.
Let χo denote the share of world oil production due to country o,
χo =
Yoo
.
Yoa + Yoo
The share of world oil consumption due to country o is given by θo ,
θo =
Oo
.
Oa + Oo
Note that since country a imports oil from country o, χo > θo .
The market clearing condition for the oil market is given by
Oa + Oo = Yoa + Yoo .
(2)
The world oil price, Po , adjusts to ensure this condition holds.
The revenue country o receives from exporting oil to country a is given
by Po (Yoo − Oo ). This can also be re-written as Po (Oa − Yoa ), which is the
oil import bill for country a.
7
For the non-oil good, we assume country a is endowed with a fixed supply
given by Yaa . The non-oil good is either consumed or used as an input to
produce oil (rigs, services, so on). Let Aac and Aoc be amounts consumed by
country a and country o, respectively, while Aay and Aoy are the quantities of
the non-oil good used in the production of oil. The use of the non-oil good in
the production of oil implies that for both countries there is an opportunity
cost of producing more oil.3 The market clearing condition for non-oil good
is given by
Yaa = Aac + Aay + Aoc + Aoy .
(3)
3.2
Effects of the subsidy on the oil market
Consider a policy in country o which changes the domestic price of fuel
products, Ps . We consider an unspecified percent change in the price, %∆Ps .
In the context of the simple model above, the change in oil consumption in
country o would be given by
%∆Oo = − %∆Ps .
(4)
Not surprisingly, a reduction in Ps would lead to an increase in consumption
of oil products in country o, with the size of the response being determined
by the price-elasticity of demand.
In turn, the increase in demand for oil by country o will result in a change
in the world market price of oil, Po . From equation (2), the change in the
world price of oil must satisfy:
−(1 − θo )%∆Po − θo %∆Ps = [(1 − χo )η a + χo η o ] %∆Po .
(5)
Solving (5) for %∆Po yields:
−θo %∆Ps .
(6)
(1 − θo ) + (1 − χo )η a + χo η o
Thus, a change in the subsidized price moves the world oil price in the
opposite direction, as the world price adjusts to clear the oil market. As a
result of higher world oil prices, consumption of oil in country a is crowded
out by the subsidy,
%∆Po =
%∆Oa = (1 −
θo )
θo %∆Ps .
+ (1 − χo )η a + χo η o
(7)
3
One can obviously consider other resources that might be used in the production of oil,
such as labor, non-traded services, etc. All of these would introduce the notion that there
is an opportunity cost associated with changing the supply of oil, and would introduce
various distortions in the model.
8
The size of the changes in Po and Oa depend upon the elasticities of
demand and supply as well as the shares of the two countries in the consumption and production of oil. In general, the larger the share of country
o in world oil usage (θo ), the bigger the effect a change in the subsidized
price has on the world oil price. Intuitively, if the subsidizing countries are
large, then even a small change in Ps will have a large effect on the world
price of oil. On the other hand, the larger the elasticity of world oil supply
((1 − χo )η a + χo η o ), the smaller effect a change in the subsidized price has
on the world oil price. With supply more responsive, less crowding out of
country a’s oil consumption needs to occur to clear the market, and, as a
result, prices need to change by less in response to the increase in oil demand
by the subsidizing country.
Finally, total world consumption of oil may also be affected when Ps
changes. Note, though, that the supply elasticities play a key role in this
result. If supply elasticities are zero then increases or decreases in Ps merely
re-allocate consumption across countries but have no impact on overall consumption. When η a , η o or both are non-zero reductions in Ps would increase
world oil consumption.
3.3
Effects of the subsidy on export revenues and trade
Since the subsidy affects the world price of oil, Po , it has implications for the
terms of trade between the two countries. More specifically, as an exporter
of oil, country o’s terms of trade are positively (negatively) affected by the
presence (removal) of a subsidy. This may have implications for country o’s
oil export revenues and its ability to purchase non-oil goods from a.
The amount of the non-oil good that country o can purchase depends on
the revenue it receives from exporting oil to a. The current account equation
for country o links up these two quantities and is given by:
Po (Oa − Yoa ) = Aoc + Aoy .
(8)
A change in the subsidized price Ps will change country o’s export revenue
for two reasons. First, it will affect the price o receives for the oil it exports.
Second, the subsidy will also affect the quantity of oil that country a imports.
The total impact of these two effects on the oil import bill of a will depend
upon how responsive country a’s production and consumption of oil is to
the change in Po .
A convenient way to think about the total impact is to consider the price
elasticity of oil import demand in country a, which we define as ξ a . The
9
response of export revenue to changes in the world price of oil is then given
by
%∆[Po (Oa − Yoa )] = (1 − ξ a ) %∆Po .
(9)
By definition, whether oil export revenue for country o rises or falls when the
market oil price rises depends on whether ξ a is less than or greater than 1.
If import demand is inelastic (ξ a < 1) then a rise in Po will increase country
o’s oil export revenue, as the increase in Po more than compensates for the
decline in the quantity of oil imported by country a. If import demand is
elastic (ξ a > 1) the opposite occurs and country o’s export revenue falls
when Po increases.
The solution for ξ a can be derived using the left-hand side of equation
(8). Formally, the import demand elasticity is given by
ξa =
(1 − θo ) + (1 − χo )η a
.
χo − θ o
(10)
Note that the import demand elasticity depends not just on country a’s oil
demand elasticity, but also on country a’s elasticity of supply and the shares
of country a in world oil use and production. Only in the special case where
country a imports all of its oil (χo = 1) is ξ a = .
Small elasticities of demand () and supply (η a ) make it more likely that
import demand is inelastic. Similarly, the more country a relies on imports
of oil (the higher χo is relative to θo ), the more likely import demand will be
inelastic. While empirical evidence suggests that the elasticity of demand
for oil () is less than one, this does not necessarily guarantee that country
o’s oil export revenues will rise when Po rises.
What happens to oil export revenue is important because it helps determine how much of the non-oil good country o can purchase. If the imposition
of the subsidy (which increases the world price of oil) raises oil export revenue (ξ a < 1), income is transferred from a to o which allows country o to
purchase more of the non-oil good. On the other hand, if oil export revenues fall when the price of oil increases (ξ a > 1), country o would be able
to purchase less of the non-oil good.
3.4
Effects of the subsidy on welfare
The previous results have interesting implications for the welfare effects of
the subsidy on country o. More specifically, when ξ a < 1 the subsidy, by
raising the world price of oil, inflates country o’s oil export revenue. This
creates a benefit for country o at the expense of country a and allows o
10
to increase its purchases of the non-oil good. In this case, the subsidy
may be welfare enhancing for country o if it allows them to increase their
consumption of non-oil goods.
We note, however, that an increase in export revenue is not sufficient to
ensure that country o will actually be better off. To the extent that country
o produces more oil, this increases the costs associated with producing oil,
given by Aoy . The increase in costs offset the benefit that accrues to o from
the inflated world price of oil because they spend part of the extra income
on importing goods used to produce oil instead of on consumption goods.
When ξ a ≥ 1, it seems more likely that the subsidy will reduce welfare
in country o. In that case, the increase in domestic consumption of oil
that the subsidy brings about would have to be met with a decline in the
consumption of the non-oil good.
The effect of the subsidy on country a appears likely to be negative,
especially if ξ a ≤ 1. The subsidy, by raising the world oil price, crowds out
the consumption of oil in a. Furthermore, to the extent that country a ends
up increasing its domestic oil production, the quantity of the non-oil good
used in production of oil (Aay ) will rise, leaving fewer resources available for
consumption. When ξ a < 1, the subsidy also inflates country a’s oil import
bill, transferring income from a to o. If ξ a > 1, this effect works to the
benefit of a, but we suspect that this will be relatively more important for
o than a.
3.5
Summary
The results in this section highlight several channels through which fuel subsidies can distort both the oil market and the world economy. The solutions
suggest that the quantitative importance of the subsidies will depend upon
factors such as how much oil the subsidizing countries consume, how much
oil the non-subsidizing countries produce, the values of elasticities of demand
and supply in the two countries, and how large the subsidies are.
We have also found that the various channels may have different implications for the two countries. For country o, at least one of the channels
may operate as a benefit from their perspective, at the expense of country a.
The strength of this channel depends upon the price elasticity of oil import
demand in country a, the value of which is determined by how much oil
country a produces and consumes relative to country o, as well as on country a’s elasticities of oil supply and demand. If import demand is inelastic
enough, the subsidy could actually be welfare enhancing for country o.
To help with the exposition of the simple model, we wrote the model as if
11
the country shares in production and consumption of oil and the elasticities
of supply and demand were primitives. However, it is clear that quantitative
values of these parameters are in fact related to one another. In the next
section we introduce a more sophisticated general equilibrium model where
these key share and elasticity parameters are related to underlying parameters describing tastes and technology. We calibrate the general equilibrium
model to match various features of the data, including those outlined in
section 2. We then use this model to quantify the impacts of the subsidies
on both countries.
4
Model and results
We now introduce a two-country dynamic general equilibrium model. In this
model we make the production of both oil and non-oil goods endogenous.
As before, the countries are denoted as a and o, and superscripts are used to
distinguish the countries. A representative firm in country a produces the
non-oil good using labor, capital, and oil as inputs. Oil is produced in both
countries using the non-oil good as an input. As before, country a is a net
importer of oil.
In our policy experiments, we work primarily with the steady state version of the model. However, we introduce the fully dynamic version here
to describe where the steady state equations come from. At certain points
in the discussion we simplify the presentation of the equations for brevity’s
sake. All of the equations from the model, along with their steady state
versions, can be found in the appendix.
4.1
4.1.1
Country a
The Household
A representative household in country a derives utility from the consumption
a and Aa , respectively. The household
of oil and non-oil goods, given by Oc,t
c,t
also derives dis-utility from providing labor, denoted as Nta , to the firms
that produce good A. We assume that aggregate consumption, given by Cta ,
is a CES aggregation of the two consumption goods,
h
i 1
a 1−µc 1−µc
Cta = (1 − γoa )Aac,t1−µc + (γoa )Oc,t
,
(11)
where γoa is the consumption-expenditure share of oil in country a and µc is
the inverse of the price-elasticity of demand for fuel.
12
The household maximizes lifetime utility
E0
∞
X
β
t
t=0
Cta 1−σ
Nta 1+µn
−κ
1−σ
1 + µn
!
,
(12)
where β is the discount factor, the parameter σ is the relative risk aversion
parameter, κ reflects the weight that households place on leisure relative to
consumption, and µn is the inverse of the Frisch elasticity of labor supply.
Utility is maximized subject to the budget constraint
a
a
Aac,t + Po,t Oc,t
+ AaI,t = Wta Nta + rta Kt−1
+ Πaa,t + Πao,t ,
(13)
where Po,t is the relative price of oil, AaI,t is gross investment in the capital
good, Wta is the wage, and rta is the return to capital. Households own the
firms that operate in the economy and, as a result, receive any profits from
both the oil sector, Πao,t , and the non-oil sector, Πaa,t .
Capital accumulation follows the standard law of motion
a
a
Kta − Kt−1
= AaI,t − δKt−1
.
(14)
a
Our notation implies that Kt−1
is a pre-determined state variable in the
model. When deriving first order conditions for the household’s problem we
substitute out AaI,t using the law of motion for capital.
First-order conditions for the household’s problem are given by
a
M Ua,t
= λat ,
(15)
a
M Uo,t
a
M Un,t
λat
(16)
=
=
=
Po,t λat ,
Wta λat ,
a
βEt λat+1 rt+1
(17)
+ (1 − δ) ,
(18)
a , M U a , and M U a are the marginal utilities for the consumpwhere M Ua,t
o,t
n,t
tion of the non-oil good, the oil good, and labor, respectively, and λat is the
multiplier on the budget constraint.
4.1.2
Production of the non-oil good
Production of the non-oil good is done by a representative firm in country a
using capital, labor, and oil. In the production function, capital and oil are
combined to produce a capital service which is then combined with labor to
produce good A. The exact production function is
a
a
Ya,t
= Zy,t
Nta
α
a a 1−ν
a 1−ν 1−α
1−ν
ωy Kt−1 + 1 − ωya Oy,t
,
13
(19)
a is production of the non-oil good in country a, Z a is total factor
where Ya,t
y,t
a is oil used by the firm in country a. The parameter
productivity, and Oy,t
α is the share of labor in gross-output and ν is the elasticity of substitution
between oil and the capital in the production of capital service.4
The representative producer of the non-oil good maximizes profit
a
a
a
Πat = Ya,t
− rta Kt−1
− Wta Nta − Po,t Oy,t
.
(20)
The first order conditions are:
a
M Pn,t
= Wta ,
(21)
a
M Pk,t
a
M Po,t
(22)
=
rta ,
= Po,t .
(23)
a is the marginal product of output with respect to capital, labor,
Here M Pi,t
and oil for i = k, n, o, respectively.
4.1.3
Production of oil
A profit maximizing firm produces oil in country a. Oil production costs are
given by Aay,t and are an increasing function of oil output. The oil producing
firm in country a chooses its production level to maximize:
a
Πao,t = Po,t Yo,t
− Aay,t ,
where
Aay,t
(24)
1+ η1a
= κa
a)
(Yo,t
1+
1
ηa
.
(25)
The production costs are in terms of the non-oil good A. One can think
of this as the drilling rigs, oil equipment, or any non-oil good that is used
to produce oil. Although we don’t model depletion, costs increase with
increased oil production, reflecting the difficulty of finding additional oil as
more oil is produced. The optimal quantity of oil production satisfies:
1
a ηa
Po,t = κa (Yo,t
) .
(26)
Using equation (A.4), one observes that country a’s elasticity of oil supply
is given by η a .5
4
Like much of the macroeconomics literature, we assume the elasticity of substitution
between labor and the capital service is one.
5
The cost function also implies that the higher the elasticity of supply, the lower the
marginal cost of producing a given amount of oil.
14
4.2
4.2.1
Country o
The Household
Like that in country a, the representative household in country o derives
utility from the consumption of the non-oil and oil goods, given by Aoc,t and
o , respectively. As in country a, these two goods are aggregated using
Oc,t
a CES production function to generate aggregate consumption, Cto . The
household maximizes
∞
X
(C o )1−σ
βt t
E0
,
(27)
1−σ
t=0
with
i 1
h
o 1−µc 1−µc
Cto = (1 − γoo )Aoc,t1−µc + (γoo )Oc,t
,
(28)
and subject to the budget constraint
o
Aoc,t + Ps,t Oc,t
= Tt .
(29)
Here Ps,t is the potentially subsidized price of oil products in country o
and Tt are lump-sum transfers from the government to the representative
household.
The first-order conditions for the household are
o
M Ua,t
= λot ,
(30)
o
M Uo,t
(31)
=
Ps,t λot ,
o and M U o are the marginal utilities for the consumption of the
where M Ua,t
o,t
manufactured good and the oil good, respectively, and λot is the multiplier
on the budget constraint.
4.2.2
Production of oil
In many of the countries found in Table 1 the government is heavily involved
in the production of oil, often through a national oil company. In line with
this we assume the government, through a national oil company, controls the
production of oil in country o. The company sells a portion of its production
domestically at the subsidized prices Pts , exports the remainder at the world
price Pto , and then transfers its revenue to the government.
o , to maximize:
The oil producer hence chooses production, Yo,t
o
o
o
Πot = Po,t (Yo,t
− Oc,t
) + Ps,t Oc,t
− Aoy,t ,
15
(32)
where the cost function is similar to country a’s:
Aoy,t
= κo
o )
(Yo,t
1+
1+ η1o
1
ηo
.
(33)
The optimal quantity of production satisfies:
1
o ηo
Po,t = κo (Yo,t
) ,
(34)
where the elasticity of supply is given by η o .
Oil revenues are infused into the economy in a lump-sum manner, with
the value given by Tt . Each period the government must satisfy its budget
constraint,
o
o
Pto Yoo − Oc,t
+ Pts Oc,t
− Aoy,t = Tt .
(35)
The transfer Tt in the household budget constraint is equal to net revenue
from oil production, taking into account the subsidy and the costs of production. Note that if the government decides to sell oil at a reduced price
to domestic households this lowers its overall revenue from the sale of oil,
holding all else constant. This means that there is no free lunch from the
subsidy as higher subsides mean lower distributions of income flow to the
representative household.
Note also that at the aggregate, the subsidy does not, by itself, directly
affect national income in country o. This can be seen by combining the
government budget constraint, equation (35), with the household budget
constraint, equation (29). This produces the current account equation for
country o
o
o
Pto (Yo,t
− Oc,t
) = Aoc,t + Aoy,t .
(36)
The subsidy only affects the income available to country o indirectly by
changing the amount of oil consumed by domestic residents, which alters
the quantity of oil available for export, by changing the world price of oil,
and by changing oil production levels, which affects the level of costs.
4.3
Market clearing and the current account
Market clearing conditions for both goods imply that total demand must
equal total supply. The market clearing condition in the oil market is
a
a
o
o
a
Oc,t
+ Oy,t
+ Oc,t
= Yo,t
+ Yo,t
.
(37)
For the non-oil good the condition is
a
Aac,t + AaI,t + Aoc,t + Aay,t + Aoy,t = Ya,t
.
16
(38)
Combining the market clearing conditions and the current account equation
for country o given by equation (36) yields a current account equation for
country a given by
a
a
a
a
Po,t Oc,t
+ Oy,t
− Yo,t
= Ya,t
− Aac,t − AaI,t − Aay,t
(39)
This equation simply states that the dollar value of the oil imported into
country a at time t must equal the dollar value of the goods it exports
to country o. The connection between imports and exports can be made
explicit by re-writing this equation as
a
a
a
Po,t Oc,t
+ Oy,t
− Yo,t
= Aoc,t + Aoy,t .
4.4
Calibration
The model is calibrated to an initial steady state that is consistent with
recent economic data. The frequency is annual. Units are chosen so that
GDP in the oil-importing countries equals 1. The steady state values of the
model’s variables are chosen so as to match a set of statistics outlined in
table 3.
We calibrate the consumption-expenditure share of oil in the oil-importing
countries at 5 percent. This is based on recent CPI-weights for the U.S., the
EU-27, and Japan. Firm use of oil products in a is set at 2 percent of GDP,
based on recent data from input-output tables for many OECD countries.
Investment spending in a is set at 20 percent of GDP. Consistent with the
data in table 2 we set the consumption of oil in the oil-exporting countries
at 13.5 percent of world consumption. Their share of world oil production
is set at 48 percent. The value of Ps is set so that the subsidized price is 34
percent of the world price.
Table 3 also lists the calibration for the model’s parameters. We choose
the discount factor to be consistent with annual real interest rates in the
U.S. Many of the other parameters are calibrated using settings frequently
found in the macro literature.
The oil-related elasticities merit further discussion. The elasticities of
substitution are calibrated to match longer-run price elasticities of demand
for fuel products. We use previous estimates in the literature to guide our
calibration. Hausman and Newey (1995) found a long-run price elasticity
near -0.80 for gasoline demand in the U.S. Yatchew and No (2001) found
a similar elasticity for Canada. Kilian and Murphy (2014) found a shortrun elasticity of global demand for oil of -0.26. Baumeister and Peersman
(2012) found estimates slightly below that. Graham and Glaister (2002)
17
surveyed estimates of short and long-run elasticities of demand for fuel.
Short-run estimates were clustered between -0.35 and -0.25, while longerrun elasticities were larger and typically closer to -0.80. Given our model’s
annual frequency and the focus on longer-run implications of subsidies, we
choose a baseline calibration for the elasticities of substitution of -0.75. We
consider several other possibilities for sensitivity analysis.
Supply elasticity estimates are sparse in the literature, but tend to be
small. Baumeister and Peersman (2012) find that recent estimates of shortrun global supply elasticity are less than 0.2. The results in Kilian and
Murphy (2012) also suggest small supply elasticities. We set our supply
elasticities to 0.3 but also consider several other possibilities for sensitivity
analysis. The elasticities are set equal across countries, consistent with the
data that two blocs have produced a relatively stable share of world oil
production.
4.5
Policy experiment
Our policy experiment is as follows. We first assume the world is in an initial
steady state consistent with our calibration and the model’s equations. We
then ask what would happen if the subsidies in country o were permanently
removed. In the context of the model, this is done by equalizing fuel prices
across countries.
We focus on the long-run impact of this policy change, i.e. we ask how the
steady state of the model is affected. Technically, we conduct a comparative
statics exercise. For each variable of interest we numerically calculate the
percent change of that variable across steady states.
4.6
Results
Our results are presented in table 4. The first column lists the variables
considered with prices first, followed by variables for country o, variables for
country a, and finally world oil consumption. The second column shows the
percent changes across steady states for the different variables.
Under the baseline, we find that the removal of the subsidy has a nontrivial impact on the world price of oil: the model predicts that prices would
decline by over 6 percent. Lower oil prices bring about a decline in oil
production of equal magnitude in both countries, as the supply elasticities
are equal. Domestic prices in o need to rise by over 175 percent to get them
equal to the new world price of oil.
The equalization of fuel prices across the two blocs of countries leads to a
18
re-allocation of oil consumption. Oil consumption declines in the subsidizing
countries by over 45 percent, while consumption by households and firms in
country a rises by about 5 percent.
In country o, the removal of the subsidy eliminates the price distortions
which had led to over-consumption of oil and and over-investment in the
oil industry. Consumers increase their consumption of good a, with nonoil consumption rising by about 15 percent. This increase occurs for two
reasons. First, the relative price of fuel in country o is now significantly
higher. Second, the fall in oil production lowers production costs and releases
some of good A that was used in the oil sector, for consumption.
In terms of GDP (non-oil) in country a, the decline in the world price of
oil leads to a small positive increase in country a’s non-oil GDP. Intuitively,
the elevated prices that were due to the subsidies being in place before the
policy change acted like an oil supply shock which reduced (non-oil) GDP
in country a. With the subsidies removed, world oil prices decline and act
like a positive oil supply shock for country a.
4.6.1
Welfare Implications
In addition to asking how variables changed across steady states, we also
calculated how steady state welfare in country a and o was affected by the
policy change. To do this, we solve for how much aggregate consumption
would need to be decreased in the new steady state (with no subsidies) in
order for welfare to be the same as in the old steady state (with subsidies).
We convert these numbers into percentages which show the welfare gain (or
loss) from removing the subsidies. If this number is positive, it means that
the country experienced a welfare gain. The opposite holds if the number is
negative. The exact details of the calculations can be found in the appendix.
The welfare results are presented in Table 4. We find that removing the
subsidies is welfare enhancing for both blocs of countries. For country a,
the welfare gain is about 0.2 percent of steady state aggregate consumption.
The welfare gains are higher for country o, which sees a gain of close to 0.9
percent.
Based on the intuition derived in Section 3, the results for country a are
not entirely surprising. The subsidy drives up the world price of oil and
essentially acts as a negative oil supply shock that reduces consumption of
oil by both households and firms in a. It also introduces other distortions as
it leads to over-production of oil in country a. When the subsidy is removed,
these distortions are eliminated, which improves welfare in a.
As discussed in Section 3, there was a possibility that removal of the
19
subsidy could either increase or decrease welfare in country o. This is due
to the fact that the subsidy artificially inflates the world price of oil, which
could raise country o’s oil export revenue. But whether this actually occurs
depends on the price elasticity of oil import demand in country a, which we
had denoted as ξ a . For our baseline calibration, equation (10) suggests an
estimate for ξ a at around 2.3, implying that removing the subsidies actually increases country o’s export revenues. As a result, country o’s welfare
improves when the subsidy is removed.
4.6.2
Varying supply and demand elasticities
The solutions in Section 3 suggest that both supply and demand elasticities
can play an important role in the results. Given that there is some uncertainty about these elasticities, we also considered a range of alternative
values for these parameters. For each alternative calibration we consider,
we repeat our policy experiment as described before.
Alternative supply elasticities
We considered four alternative values for the supply elasticities: 0.1, 0.2,
0.3, and 0.4. The results for each parameter setting are found in table 5.
We find that the less elastic the supply, the larger the decline in world oil
prices. Oil prices decline almost 8 percent when η a and η o are set to 0.1. A
larger fall in oil prices implies there is less of a price differential to be made
up by the new domestic price (Ps ) in country o. Hence, there is a smaller
percentage increase in fuel prices in o for lower supply elasticities.
The benefits of removing the subsidy are larger for country a as supply
becomes more inelastic. Oil prices fall more, and consumption of both oil
and non-oil goods rises by a larger amount, as does non-oil GDP. Not surprisingly, the welfare gains that accrue to country a from the removal of the
subsidy grow as supply becomes more inelastic.
For country o we find that the benefits of removing the subsidy decrease
as supply becomes more inelastic. Oil consumption falls by more and nonoil consumption rises by less. We also find that removing the subsidy can
actually lead to a welfare decline in country o when supply is very inelastic
(η j = 0.1). One reason is that the mis-allocation of resources devoted to
producing oil is less (supply responds less to distorted oil prices), which
reduces a potential benefit of removing the subsidy. Another reason is that
the elasticity of oil import demand in country a becomes smaller as country
a’s oil supply becomes less elastic. As a result, removing the subsidy has
less benign implications for country o’s oil export revenue.
Alternative demand elasticities
20
The demand elasticities are determined by the settings for the elasticities
of substitution. We considered alternative calibrations for the elasticities of
substitution of 0.45, 0.55, 0.65 and 0.75. We view these as plausible ranges
given the time-frame we are considering with our policy experiment and the
estimates of price elasticities found in the literature. Table 6 contains the
results for the alternative elasticities of substitution.
We find that varying the price elasticities has a minor impact on the
world price of oil. The price decline ranges from 6.1 percent to 5.7 percent.
The fact that less elastic demand generates smaller price responses is somewhat counter-intuitive and deserves further discussion. A lower elasticity of
demand has two implications for the consumption of oil. On the one hand,
it reduces the responsiveness of consumer demand in country o to changes
in their domestic price. As a result, removing the subsidy brings about
a smaller decline in their consumption, which means that oil exports from
country o also increase by less. This creates less pressure on world oil prices.
On the other hand, the lower elasticity also implies that consumers in a need
to see bigger changes in prices to get them to consume oil. Overall, country
o drives the results.
For country o, there are important quantitative and qualitative differences in the results. As demand becomes more inelastic, oil consumption
falls by less and non-oil consumption rises by less. We also find that welfare
in o is significantly affected by demand elasticities. If demand is inelastic
enough, it is possible to experience a welfare loss from removing the subsidy.
This is reminiscent of the results for low supply elasticities. As the price
elasticity of oil demand falls, so too does the price elasticity of oil import
demand for country a.
For country a we find that the implications of less elastic demand are not
as dramatic as what occurs in country o. Oil consumption rises by less, but
non-oil GDP and welfare are not significantly affected. We do note, however,
the non-oil consumption rises by more as demand becomes less elastic. This
result is due in part to the lower oil import elasticities, which lead to greater
consumption of non-oil goods (coming at the expense of country o).
4.6.3
Other factors that affect welfare
Analytical results in Section 3 also suggested that the share of world oil
consumption due to o, denoted by θo , and the share of world oil production
due to o, denoted as χo could be important. The values of θo and χo jointly
determine the degree to which country o is a net exporter and also influence
the import elasticity of demand in country a, ξ a . The value of θo also plays
21
a key role in determining how big of an impact subsidies have on the world
price of oil.
It interesting to ask how varying these two parameters would influence
the results. To do so we consider several different cases where we vary the
values of χo and θo . To motivate some different calibrations we turn to the
data. We first consider a calibration for θo of 0.03 and χo of 0.13. These are
motivated by the data for the largest single producer and consumer among
the 24 countries: Saudi Arabia. Our second calibration sets θo to 0.082
and χo to .23, consistent with the data for the top five consumers amongst
the group of 24: Egypt, Indonesia, Iran, Saudi Arabia, and Venezuela. In
each case, we re-calibrate the model and repeat our policy experiment of
removing the subsidies. Our results are contained in table 7.
We find that the change in the world price of oil is larger as more countries are included in the exporting group. This is not surprising, given that
their share of world oil consumption rises. We also find that country a is
more positively affected by the removal of the subsidy as the subsidizing
group becomes a larger producer and consumer of oil. When country o only
consumes 3 percent of the world’s oil, the price impact of removing subsidies are relatively small, and therefore the impact this policy change has
on country a is small. These impacts become larger as more countries are
added in.
From country o’s perspective, we find that the results are qualitatively
similar to the baseline case in that oil consumption falls, non-oil consumption rises, and country o sees welfare gains from removing the subsidy in
all three cases. We note that the gains are significantly larger in the two
alternative calibrations. This is in line with the intuition from Section 3;
in both alternative calibrations, the import elasticity of demand in country
a is significantly higher than the baseline calibration. This makes it much
more likely that removing the subsidy increases welfare in country o.
We note, though, that the above welfare results are mixing together
the implications of varying χo and θo . To better understand the individual
affects of varying production and consumption shares, we varied χo while
holding θo fixed at the baseline calibration of 0.135 and using the baseline
calibration for the elasticities of oil supply and demand. We find that there
is a critical value of χo around 0.52 where the welfare effect of removing the
subsidies on country o switches from positive to negative; values of χo above
0.52 imply negative welfare effects of removing the subsidy while values
below 0.52 lead to welfare gains. As χo increases, the import elasticity
of demand in country a declines and the costs to country o of removing
the subsidy increase. Eventually this channel dominates the outcome and
22
welfare declines when the subsidy is removed. Similarly, we varied θo while
holding χo fixed at the benchmark value of 0.48. Here also we find a critical
value of θo of around 0.05 where the welfare effects of removing the subsidies
switches from positive to negative; values of θo below 0.05 result in a decline
in welfare for country o while values above 0.05 lead to welfare gains.
5
Concluding Remarks
In this paper, we used a two country, two good, general equilibrium model
to examine the impact that oil price subsidies have on the oil market and the
trade of non-oil goods. We calibrated the model to match the most recent
data. In our baseline case, we found that the removal of subsidies resulted
in a six percent decline in oil prices and was welfare enhancing for both the
importing and exporting countries.
We also showed how the effects of removing existing subsidies depend on
oil supply and demand elasticities, as well as the share of world oil production
and consumption due to the subsidizers. The welfare effects on oil importing
countries were unambiguously positive for all the cases considered. However,
in certain cases removing the subsidies was actually found to be welfare
reducing for the subsidizing countries. This occurs if oil supply or demand
is relatively inelastic, and when the subsidizers produce a large enough share
of the world’s oil supply relative to what they consume.
Several avenues for future research suggest themselves. First, while our
model was explicitly dynamic, our examination of the effect of removing
oil price subsidies was entirely steady state. The transition from initial
steady state, where there are substantial subsidies, to a new steady state in
which the subsidies are removed may give rise to intertemporal trade-offs
that might alter the welfare comparisons. Along similar lines, a richer and
dynamic model of oil supply might suggest additional intertemporal tradeoffs. A closer examination of how these subsidies are financed (here we
assumed they were financed by lump-sum transfers/taxes) might also alter
welfare implications of the subsidies.
A final issue of interest may be the reduction of carbon emissions associated with the removal of subsidies. By changing the level of global oil
consumption, oil product subsidies also affect global carbon emissions and
local pollution levels. A very rough calculation using our baseline scenario
puts the decline in global CO2 emissions from the removal of the subsidies
at 0.75% of total CO2 emissions in 2012.6 Another avenue of research would
6
The appendix provides the details of this calculation.
23
be to undertake a more rigorous analysis of this issue.
24
References
[1] Baumeister, Christiane and Gert Peersman (2013). “The role of timevarying price elasticities in accounting for volatility changes in the crude
oil market.” Journal of Applied Econometrics 28 (7): 1087 – 1109.
[2] Coady, David, Moatz El-Said, Robert Gillingham, Kangni Kpodar,
Paulo Medas, and David Newhouse (2006). “The magnitude and distribution of fuel subsidies: evidence from Bolivia, Ghana, Jordan, Mali,
and Sri Lanka.” IMF Working Paper WP/06/247.
[3] Deutsche Gesellschaft fur Internationale Zusammenarbeit (2011). International Fuel Prices Survey 2010/2011.
[4] Graham, Daniel J. and Stephen Glaister (2002). “The Demand for Automobile Fuel: A Survey of Elasticities.” Journal of Transport Economics and Policy 36 (1): 1 – 26
[5] Hartley, Peter and Kenneth B. Medlock III (2008). “A model of the operation and development of a national oil company.” Energy Economics
30 (5): 2459 – 2485
[6] Hausman, J. and W. Newey (1995). “Nonparametric Estimation of Exact Consumer Surplus and Deadweight Loss.” Econometrica 63 (6):
1445 – 1476
[7] IEA (2010). World Energy Outlook 2010.
[8] Kilian, Lutz and Daniel P. Murphy (2014). “The role of inventories
and speculative trading in the global market for crude oil.” Journal of
Applied Econometrics 29 (3): 454 – 478
[9] Kpodar, Kangni (2006). “Distributional Effects of Oil Price Changes on
Household Expenditures: Evidence from Mali.” IMF Working Paper,
WP/06/91.
[10] Plante, Michael (2014).“The long-run macroeconomic impact of fuel
subsidies.” Journal of Development Economics 107: 129-143.
[11] Yatchew, Adonis and Joungyeo Angela No (2001). “Household Gasoline
Demand in Canada.” Econometrica 69 (6): 1697 – 1709
25
Table 1: Countries identified as subsidizers
Algeria
Libya
Angola
Malaysia
Azerbaijan Nigeria
Bahrain
Oman
Bolivia
Qatar
Brunei
Saudi Arabia
Ecuador
Sudan
Egypt
Syria
Indonesia
Turkmenistan
Iran
United Arab Emirates
Iraq
Venezuela
Kuwait
Yemen
26
Table 2: Statistics about the 24 countries
Share of world Share of world
Year oil consumption oil production
1992
9.5
46.1
1993
9.9
47.3
1994
10.0
47.6
1995
10.0
47.7
1996
10.0
47.5
1997
10.2
48.0
1998
10.2
48.8
1999
10.2
48.1
2000
10.4
48.9
2001
10.8
47.9
2002
11.0
46.2
2003
11.1
46.6
2004
11.3
47.8
2005
11.6
48.9
2006
11.8
48.6
2007
12.1
48.4
2008
12.9
49.4
2009
13.0
48.1
2010
13.1
48.3
2011
13.4
48.1
2012
13.5
47.9
27
Table 3: Steady state moments and parameter values
Investment in a (AaI )
20 percent of a’s GDP
Consumption-expenditure share of fuel in a
5 percent
a
2 percent of a’s GDP
Firm use of oil in a (Po Oy )
Consumption of fuel in o
13.5 percent of world consumption
Oil production in o
48 percent of world production
Ratio of subsidized price to world price
(η a ,
ηo)
Elasticity of supply
Discount factor (β)
Elasticities of substitution ( µ1c , ν1 )
Risk aversion parameter (σ)
Frisch elasticity of labor supply ( µ1n )
Labor share in production of a (α)
28
Ps
Po
.34
.30
.96
.75
2
1
.70
Table 4: Effects of removing the oil subsidies in baseline model
Variables
Baseline
Prices
market oil price (Po )
subsidized oil price (Ps )
-6.1
176.0
Country o variables
oil production (Yoo )
oil consumption (Oco )
consumption of good A (Aoc )
transfers (T)
welfare
-1.9
-45.9
15.9
21.4
0.86
Country a variables
oil production (Yoa )
oil used in consumption (Oca )
oil used in production(Oya )
consumption of good A (Aac )
non-oil GDP
welfare
-1.9
4.9
5.2
0.004
0.23
0.23
World variables
World oil consumption
-1.9
Note: Variables are in percent change across steady states. The new steady
state is the one without subsidies. Welfare is in consumption-equivalent
percentages.
29
Table 5: Effects of removing oil subsidies for different elasticities of supply
Variables
η j = 0.4
η j = 0.3
η j = 0.2 η j = 0.1
(Baseline)
Prices
market oil price (Po )
subsidized oil price (Ps )
-5.5
178.0
-6.1
176.0
-6.9
173.8
-7.9
171.0
Country o variables
oil production (Yoo )
oil consumption (Oco )
consumption of good A (Aoc )
transfers (T)
welfare
-2.2
-44.9
18.6
24.8
1.64
-1.9
-45.9
15.9
21.4
0.86
-1.4
-46.8
13.3
18.0
0.03
-0.8
-47.6
10.7
14.8
-0.87
Country a variables
oil production (Yoa )
oil used in consumption (Oca )
oil used in production(Oya )
consumption of good A (Aac )
non-oil GDP
welfare
-2.2
4.3
4.6
0.004
0.20
0.20
-1.9
4.9
5.2
0.004
0.23
0.23
-1.4
5.5
5.9
0.005
0.26
0.26
-0.8
6.3
6.8
0.006
0.29
0.29
-2.2
-1.9
-1.4
-0.8
World variables
World oil consumption
Note: Variables are in percent change across steady states. The new steady
state is the one without subsidies. Welfare is in consumption-equivalent
percentages.
30
Table 6: Effects of removing the oil subsidies for different demand elasticities
Variables
.75
.65
.55
.45
(Baseline)
Prices
market oil price (Po )
subsidized oil price (Ps )
Country o variables
oil production (Yoo )
oil consumption (Oco )
consumption of good A (Aoc )
transfers (T)
welfare
Country a variables
oil production (Yoa )
oil used in consumption (Oca )
oil used in production(Oya )
consumption of good A (Aac )
non-oil GDP
welfare
World variables
World oil consumption
-6.1
176.0
-6.1
176.3
-5.9
176.7
-5.7
177.4
-1.9
-45.9
15.9
21.4
0.86
-1.9
-41.3
13.5
21.5
0.14
-1.8
-36.5
11.2
21.7
-0.54
-1.7
-31.3
8.7
22.1
-1.15
-1.9
4.9
5.2
0.004
0.23
0.23
-1.9
4.2
4.5
0.036
0.23
0.23
-1.8
3.5
3.8
0.067
0.24
0.22
-1.7
2.8
3.1
0.094
0.24
0.22
-1.9
-1.9
-1.8
-1.7
Note: Variables are in percent change across steady states. The new steady
state is the one without subsidies. Welfare is in consumption-equivalent
percentages.
31
Table 7: Effects of removing oil subsidies for alternative shares of oil consumption and production
Variables
Saudi Top 5 consumers Baseline
Share of world consumption (θo )
Share of world production (χo )
3%
13%
8.2%
23%
13.5%
48%
Prices
market oil price (Po )
subsidized oil price (Ps )
-1.3
190.2
-3.3
184.5
-6.2
176
Country o variables
oil production (Yoo )
oil consumption (Oco )
consumption of good A (Aoc )
transfers (T)
welfare
-0.4
-47.0
18.0
22.5
4.96
-1.0
-41.0
29.2
38.0
5.77
-1.9
-45.9
15.9
21.4
0.86
Country a variables
oil production (Yoa )
oil used in consumption (Oca )
oil used in production(Oya )
consumption of good A (Aac )
non-oil GDP
welfare
-0.4
1.0
1.1
-0.01
0.07
0.02
-1.0
2.5
2.7
-0.02
0.16
0.06
-1.9
4.9
5.2
0.00
0.23
0.23
Note: Variables are in percent change across steady states. The new steady
state is the one without subsidies. Welfare is in consumption-equivalent
percentages.
32
Figure 1: Ratio of subsidized prices to U.S. prices
33
A
Appendix (Not for publication)
A.1
Data sources
• Algeria - OPEC Annual Statistical Bulletins
• Angola - World Bank data
• Azerbaijan - World Bank data
• Bahrain - World Bank data
• Bolivia - World Bank data
• Brunei - World Bank data
• Ecuador - World Bank data
• Egypt - World Bank data
• Indonesia - OPEC Annual Statistical Bulletins (1990 - 2008), media
reports on government announced fuel price changes (2008 - 2012)
• Iran - OPEC Annual Statistical Bulletins
• Iraq - GIZ International Fuel Prices survey, IMF, OPEC Annual Statistical Bulletins
• Kuwait - OPEC Annual Statistical Bulletins
• Libya - OPEC Annual Statistical Bulletins
• Malaysia - World Bank data
• Nigeria - OPEC Annual Statistical Bulletins
• Oman - World Bank data
• Qatar - OPEC Annual Statistical Bulletins
• Saudi Arabia - OPEC Annual Statistical Bulletins
• Sudan - World Bank data
• Syria - World Bank data
• Turkmenistan - World Bank data
34
• United Arab Emirates - OPEC Annual Statistical Bulletins
• Venezuela - OPEC Annual Statistical Bulletins
• Yemen - World Bank data
35
A.2
Calculating the welfare changes across steady states
Suppose X1 and X2 are the steady state values of variable X in the original
and the new steady state, respectively. Then the change in aggregate welfare
across steady states for country a is given by
a 1−σ
a 1−σ
1
(C2 )
(C1 )
(N2a )1+µn
(N1a )1+µn
−
.
−κ
−κ
1−β
1−σ
1 + µn
1−σ
1 + µn
The change in welfare in country o can be calculated similarly.
Looking at the change in aggregate welfare across steady states is not
very informative because of the units. To make the comparisons more concrete, we solve for how much aggregate consumption in the new steady state
would need to be increased or decreased, in percentage points, to make welfare equal across the two steady states. Mathematically we solve for ω in
the following equation,
("
# "
#)
(ωC2a )1−σ
(N2a )1+µn
(N1a )1+µn
(C1a )1−σ
−κ
−κ
−
= 0.
1−σ
1 + µn
1−σ
1 + µn
In general ω will be non-zero as welfare will be higher or lower across steady
states. The welfare losses are calculated as
Wl = 100 ∗ (1 − ω) .
Wl will be negative when ω > 1, which occurs when aggregate welfare
is lower in the new steady state. Aggregate consumption would need to be
increased by Wl percent to get utility in the new steady state back up to its
initial level in the old steady state.
On the flip side, Wl will be positive when ω < 1, which occurs when
aggregate welfare is higher in the new steady state. In that case, aggregate
consumption would need to be lowered by Wl percent to get utility in the
new steady state back down its lower level in the old steady state.
36
A.3
Carbon calculations
Our estimate of a 0.75% reduction in carbon emissions is a very rough calculation based on the following numbers.
Crude oil energy content (Source: EIA)
1 bbl of crude = 5.8MMBtu
Crude oil emissions (Source: EIA)
164.3 lbs of CO2 per MMBtu
Global carbon emissions (Source: http://co2now.org/current-co2/co2Now/global-carbon-emissions.html)
35.6 * 109 metric tons of CO2 in 2012
Calculations
2012 world consumption: 89.17 mb/d (Source: EIA)
1.9% decline in consumption = 1.69 mb/d decline = 616,850,000 bbl
616.85 * 106 barrels * 5,800,000 Btu/barrel = 3577.7 * 106 MMBtu
3577.7 * 106 MMBtu * 164.3 lbs CO2 /MMBtu = 587.82 * 109 lbs CO2
1 metric ton = 2204 lbs
266.71 * 106 metric tons
Percent reduction
(100*(266.71*106 )/(35.6*109 )) = .75%
37
A.4
Model equations
First order conditions for household in a
1−σ
a 1−µc 1−µc −1
(1 − γoa )(Aac,t )1−µc + (γoa )(Oc,t
)
(1 − γoa )(Aac,t )−µc = λat ,
1−σ
a 1−µc 1−µc −1 a
a −µc
(1 − γoa )(Aac,t )1−µc + (γoa )(Oc,t
)
γo (Oc,t
)
= Po,t λat ,
κ(Nta )µc = Wta λat ,
a
λat = βEt λat+1 rt+1
+ (1 − δ).
Law of motion for capital
a
a
Kta − Kt−1
= AaI,t − δKt−1
.
Production function for good a
a
a
Ya,t
= Zy,t
Nta
α
a 1−ν 1−α
a 1−ν
1−ν
+ 1 − ωya Oy,t
ωya Kt−1
.
First order conditions for the firm
α
a
(1 − α)Ya,t
(1 −
a
α)Ya,t
a
Ya,t
= Wta
Nta
a )−ν
ωya (Kt−1
a 1−ν = rta
a 1−ν
ωya Kt−1
+ 1 − ωya Oy,t
a −ν
(1 − ωya )Oy,t
a 1−ν = Po,t
a 1−ν
+ 1 − ωya Oy,t
ωya Kt−1
Costs in the oil sector in country a
Aay,t
= κa
a)
(Yo,t
1+ η1a
1+
1
ηa
.
First order condition for the oil sector in a
1
a ηa
Po,t = κa (Yo,t
) .
Market clearing condition for good A
a
Aac,t + AaI,t + Aay,t + Aoc,t + Aoy,t = Ya,t
.
38
Market clearing condition for the oil market
a
a
o
o
a
Oc,t
+ Oy,t
+ Oc,t
= Yo,t
+ Yo,t
.
Current account equation for country a
a
a
a
a
Po,t Oc,t
+ Oy,t
− Yo,t
= Ya,t
− Aac,t − AaI,t − Aay,t .
First order conditions for household in o
o 1−µc
(1 − γoo )(Aoc,t )1−µc + (γoo )(Oc,t
)
1−σ
1−µc
−1
(1 − γoo )(Aoc,t )−µc = λo,t ,
1−σ
o 1−µc 1−µc −1 o
o −µc
)
= Pts λo,t
(1 − γoo )(Aoc,t )1−µc + (γoo )(Oc,t
γo (Oc,t
)
Costs in the oil sector in country o
Aoy,t = κo
1+ η1o
o )
(Yo,t
1+
1
ηo
.
First order condition for the oil sector in o
1
o ηo
Po,t = κo (Yo,t
) .
Government budget constraint in country o
o
o
Po,t Yoo − Oc,t
+ Ps,t Oc,t
− Aoy,t = Tt .
A.5
Steady state equations
(1 − γoa )(Aac )1−µc + (γoa )(Oca )1−µc
1−σ
1−µc
−1
(1 − γoa )(Aac )−µc = λa ,
1−σ −1
(1 − γoa )(Aac )1−µc + (γoa )(Oca )1−µc 1−µc γoa (Oca )−µc = P o λa ,
κN a
µc
= W a λa ,
1
− 1 + δ = ra .
β
δK a = AaI .
Yaa = Zya N a
α
ωya K a
1−ν
Ya
α aa
N
+ 1 − ωya Oya
= Wa
39
1−ν
1−α
1−ν
,
(1 − α)Yaa
(1 −
ωya (K a )−ν
= ra
ωya (K a )1−ν + 1 − ωya (Oya )1−ν
α)Yaa
(1 − ωya )Oya
ωya K a
Aay
1−ν
−ν
+ 1 − ωya Oya
1−ν
= Po
1+ η1a
(Y a )
= κa o
1+
1
ηa
.
1
Po = κa (Yoa ) ηa .
Aac + AaI + Aay + Aoc + Aoy = Yaa
Oca + Oya + Oco = Yoo + Yoa
Po (Oca − Yoa ) = Yaa − Aac − AaI − Aay .
1−σ −1
(1 − γoo )(Aoc )1−µc + (γoo )(Oco )1−µc 1−µc (1 − γoo )(Aoc )−µc = λo ,
1−σ −1
(1 − γoo )(Aoc )1−µc + (γoo )(Oco )1−µc 1−µc γoo (Oco )−µc = Ps λo ,
Po (Yoo − Oco ) + Ps Oco − Aoy = T.
40